三角函数比值演示器
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①本范例演示根据用户输入的三角函数比值(正弦、余弦、正切等),动态绘制标准位置角对应的直角三角形及相关图形;②涉及核心数学概念包括三角函数定义、直角三角形边长关系、单位圆、坐标几何等;③作图要点运用了 GeoGebra 命令如 Denominator, Numerator, Intersect, Textfield, Dilate, Mirror, Segment, Angle, Distance, Polygon, SurdText 等,通过滑块和输入框实现用户交互;④适合高中数学教学,用于直观理解三角函数与几何图形的关联,提升空间想象能力。
GeoGebra 命令及参数
Denominator(sine) → dsineNumerator(sine) → nsineIntersect(k_1, i) → B, CTextfield(cosine) → InputBox2Textfield(sine) → InputBox1Textfield(tangent) → InputBox3Textfield(PosSec) → InputBox6Dilate(A, If[0 < j ≤ 1, 1 - j, 0], D) → A'Mirror(A', x = 0) → A''Segment(A, A') → lSegment(A, A'') → mDilate(D, If[1 < j ≤ 2, 2 - j, 0], C) → D'Mirror(D', x = 0) → D''Segment(D, D') → nSegment(E, D'') → pAngle(C, D, A) → αAngle(A, E, B) → βDilate(A, If[2 < j ≤ 3, 3 - j, 0], C) → A'_1Dilate(A, If[2 < j ≤ 3, 3 - j, 0], B) → A'_2Segment(A, A'_1) → qSegment(A, A'_2) → rDistance(D, C) → distanceDCDistance(A, C) → distanceACDistance(A, B) → distanceABDistance(E, B) → distanceEBPolygon(A, D, C) → poly1, c_1, a_1, d_1Polygon(A, B, E) → poly2, e_1, a_2, b_1Distance(D, C) → oDistance(E, B) → sNumerator(cosine) → ncosineDenominator(cosine) → dcosineIntersect(e, g) → F, GDilate(A, If[0 < j ≤ 1, 1 - j, 0], H) → A'_3Segment(A, A'_3) → f_1Dilate(H, If[1 < j ≤ 2, 2 - j, 0], F) → H'Segment(H, H') → g_1Dilate(A, If[2 < j ≤ 3, 3 - j, 0], F) → A'_4Segment(A, A'_4) → h_1Polygon(A, H, F) → poly3, f_2, a_3, h_2Mirror(A, i_1) → A'_5Mirror(H, i_1) → H'_1Mirror(F, i_1) → F'Polygon(A'_5, H'_1, F') → poly3', f', a'_5, h'_1Mirror(H, i_1) → H'_2Mirror(H', i_1) → H''Segment(H'_2, H'') → j_1Mirror(A, i_1) → A'_6Mirror(A'_4, i_1) → ISegment(A'_6, I) → l_1Angle(F, H, A) → γAngle(A, H, G) → δNumerator(tangent) → ntangentDenominator(tangent) → dtangentMirror(J, A) → J'Mirror(L, i_1) → L'Mirror(n_1, i_1) → q_1Angle(L, J, A) → εAngle(A, J, N) → ζDilate(A, If[0 < j ≤ 1, 1 - j, 0], J) → A'_7Dilate(A, If[0 < j ≤ 1, 1 - j, 0], J') → A'_8Segment(A, A'_7) → r_1Segment(A, A'_8) → s_1Dilate(J, If[1 < j ≤ 2, 2 - j, 0], L) → J'_1Dilate(J, If[1 < j ≤ 2, 2 - j, 0], N) → J'_2Segment(J, J'_1) → t_1Segment(J, J'_2) → j_2Distance(J, J'_1) → distanceJJ'1Distance(J, J'_2) → distanceJJ'2Distance(A, A'_7) → distanceAA'7Distance(A'_8, A) → distanceA'8ADilate(A, If[2 < j ≤ 3, 3 - j, 0], L) → A'_9Dilate(A, If[2 < j ≤ 3, 3 - j, 0], N) → A'_{12}Segment(A, A'_9) → k_2Segment(A, A'_{12}) → m_2Polygon(A, J, L) → poly4, l_3, a_4, j_3Polygon(A, J, N) → poly7, n_3, a_7, j_4Mirror(A, g_2) → A'_{10}Mirror(A'_9, g_2) → OSegment(A'_{10}, O) → l_2Mirror(A, r_1) → A'_{11}Mirror(A'_9, r_1) → PSegment(A'_{11}, P) → n_2Mirror(A'_{10}, s_1) → QMirror(O, s_1) → O'Segment(Q, O') → p_2Mirror(A, A) → A'_{13}Mirror(J, A) → J'_3Mirror(N, A) → N'Polygon(A'_{13}, J'_3, N') → poly7', n', a'_{13}, j'_3Mirror(J, A) → J'_4Mirror(J'_2, A) → RSegment(J'_4, R) → q_2Angle(A, J', K) → ηMirror(J, A) → J'_5Mirror(J'_1, A) → SSegment(J'_5, S) → r_2Mirror(A, A) → A'_{14}Mirror(J, A) → J'_6Mirror(L, A) → L'_1Polygon(A'_{14}, J'_6, L'_1) → poly4', l'_1, a'_{14}, j'_6Angle(M, J', A) → θDistance(A, A'_3) → distanceAA'3Distance(D, D') → distanceDD'Distance(E, D'') → distanceED''SurdText(nsine / dsine) → text5SurdText(ncosine / dcosine) → text6SurdText(ntangent / dtangent) → text7Distance(J'_5, S) → distanceJ'5S
AI 绘图提示语参考
绘制一个基于给定正弦、余弦和正切值的三角函数动态演示图。首先输入正弦值,确定单位圆上的点A,然后根据正弦值在单位圆上找到点B和C。接着输入余弦值,通过相似三角形构造点D和D',并利用镜像和缩放操作得到点A'和A''。最后,通过距离和角度计算,绘制三角形和多边形,展示正弦、余弦和正切的关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。